Volume 19, Number 2

Winter 2003 Research Bulletin of the Supercomputing Institute

Enhancing Simulations of Turbulence

Turbulence features prominently in a wide range of applications in nature and technology. It increases the drag on airplanes, improves mixing and reduces pollution inside engines, transports nutrients in the oceans, and causes buffeting inside computer disk drives. Despite their considerable importance, our ability to control or even predict turbulent flows is very limited. The equations that govern turbulent flows are well-known and are called the Navier- Stokes equations. However, it is extremely difficult to simulate turbulence by numerically solving these equations. This is because turbulent flows consist of eddying motions of various sizes, all of which would have to be represented on the computational grid. This is practical only for the simplest flows; for most flows, representing all eddies requires an impossibly large number of computational elements. As a result, turbulence simulations currently have two important limitations–they are restricted to very simple geometries and to very low Reynolds numbers. Reynolds numbers are defined as the ratio of inertial to viscous forces; airplane wings fly at Reynolds numbers of approximately 106, while current simulations are performed around 103.

As a result, such simulations are not directly applicable to the complex flows encountered in practice. The numerically generated data have largely been used to develop simpler models for practical use. However, there is considerable evidence that these simpler models lack the accuracy to predict many critically important flows, e.g., pollutant formation in engines, airplane jet exhaust noise, and the drag on aircraft at high speeds.

Professor Krishnan Mahesh and his research group in the Department of Aerospace Engineering and Mechanics are working to overcome this obstacle. Mahesh’s group is developing numerical methods and models that are, for the first time, allowing three-dimensional, unsteady turbulent simulations to be used as predictive tools for engineering flows in complex configurations. Moreover, the high fidelity of their simulations (called direct numerical simulation and largeeddy simulation) allows fundamental turbulence data to be obtained in configurations that are beyond the reach of current simulation methods. This work involves the development of novel numerical algorithms, turbulence models and large-scale simulation. Presently, this group is developing a non-dissipative, energy-conserving simulation method for unstructured grids. The result is an algorithm that is accurate enough to compute the eddying motions in turbulent flows, and robust enough to handle complex engineering geometries. Developed in collaboration with colleagues at Stanford University, this approach has made possible, for the first time, three-dimensional unsteady simulations in the exceedingly complex geometry of a Pratt & Whitney gas-turbine combustor.

Professor Mahesh’s research is currently supported by the Department of Energy, the National Science Foundation and the Office of Naval Research. Other projects being worked on by his research group include: Mr. Suman Muppidi’s research into how dilution jets inside modern gasturbine combustors mix cold air with combustion products; Mr. Pradeep Babu’s work on the mixing properties of turbulent jets and the effect of cacti geometry on their resistance to high winds; Mr. Youcheng Hou’s project concerning turbulent compressible flows; Mr. Abhijit Dande’s research into marine propeller crashback (a situation where the propeller suddenly reverses direction); and Mr. Peter Lommel’s project on near-wall turbulence.